Posts3 another derivation steady state And using the facts from last time (dropping t, t+1 and having ht+1 = ht): \[ \frac{\beta \theta_2}{\mu_2 e} = R [(1-\tau \lambda_2)nwh] - [\tau_2 (1-\Omega)\frac{wh\beta n}{e}] \] multiplying e to both sides, and taking nwh out: \[ \frac{\beta \theta_2}{\mu_2} = whn([R(1-\tau \lambda_2) e] - [\tau_2 (1-\Omega)\beta]) \] Note that \(\frac{\rho}{c_2} = \mu_2 w h \), meaning that \(wh = \frac{\rho.. 2021. 1. 7. Deriving steady state equation (ft. latex) We start from this equation: And we wish to get to (under steady state* assumption) *note: in steady state, 't' and 't+1' can be removed. eg \(h_t\) and \(h_{t+1}\) are equivalent so we can instead use \(h\) for both Before we get started, I'll denote the following as 'STUFF', as we want to preserve that part anyway: Likewise, \(\tau_2(1-\Omega_{t+1})\) will be denoted as 'STUFF2' Further, as no.. 2021. 1. 7. Modelling utility of a person over 2 phases of ages Ultimately, we get to \[U(c_{1t}, c_{2t+1},h_{t+1}) = \ln{C_{1t}} + \rho lnC_{2t+1} + \theta ln h_{t+1}\] Suppose we model a person's utility function. How do we do that? We may start from a very simple principle; that is, a person's utility is a function of their consumption. \[U(consumption) = consumption\] We can make this more elaborated, by considering the fact that a person's marginal util.. 2021. 1. 6. 이전 1 다음
